NIMCET 2009 Question Paper with solutions

Question : 36 of 120

Marks: +1, -0

From 50 students taking examination in Mathematics, Physics and Chemistry, 37 passed Mathematics, 24 Physics and 43 Chemistry. Almost 19 passed Mathematics and Physics, almost 29 Mathematics and Chemistry and almost 20 Physics and Chemistry. The largest possible number that could have passed all three examinations is

10
12
9
None of these

Validate

Solution:

Let

x

be the number of possible students who have passed all the papers.

We have the following equations and inequalities

a+b+c+d+e+f+g+x=50

....(i)

b+d+f=13

.....(ii)

a+e+f=26

....(iii)

c+d+e=7

......(iv)

c+x ≤ 19

a+x ≤ 29

b+x ≤ 20

Adding Eqs. (ii), (iii) and (iv), we get

a+b+c+d+e+f+(d + e +f)=46

⇒ \;\; d+e+f+50-g-x=46

⇒ \;\; g + x=4+d+e+f

n(M ∪ P ∪ C) \;\; =∑n(M) -∑ Σ n(M ∩ P+∩(M ∩ P ∩ C)

⇒ 50=37+24+43-19-29-20+x

⇒ \;\; x=14

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